Nonlinear viability and cycle closure of the near-surface magnetorotational-instability solar dynamo

Vasil et al. (Nature 629, 769, 2024) proposed that the solar magnetic cycle is driven by the magnetorotational instability (MRI) acting in the near-surface shear layer (NSSL), the outer roughly 5-10% of the Sun where angular velocity increases inward. Their evidence came from linear eigenmode calculations and quasi-linear saturation estimates with enhanced turbulent diffusivities (effective Reynolds and magnetic Reynolds numbers $\mathrm{Re}=\mathrm{Rm}\approx 1500$ and magnetic Prandtl number $\mathrm{Pm}=1$) and reduced physics, leaving open the decisive question: can this MRI dynamo operate and self-consistently sustain the full poloidal-to-toroidal-to-poloidal magnetic cycle under fully nonlinear, turbulent, solar-realistic conditions? The problem requires (i) fully nonlinear three-dimensional stratified magnetohydrodynamic simulations of the NSSL, with convective driving, establishing whether the MRI operates and saturates at solar-like amplitudes as turbulent diffusivities, Reynolds and magnetic Prandtl numbers, and magnetic boundary conditions (open versus closed magnetic-helicity fluxes) are varied toward solar values; and (ii) identification and demonstration of the nonlinear mechanism that regenerates the poloidal field, closing the cycle in the presence of strong convection. The source further proposes observational tests through joint helioseismic inversions of the predicted correlations between torsional-oscillation flow perturbations and subsurface magnetic fields, and of the poloidal-field strength window that permits MRI. Later mean-field modeling suggests turbulent diffusivity may suppress NSSL MRI, and one helioseismic analysis favors a deeper dynamo origin, but no fully nonlinear demonstration or refutation exists, so the core remains open.

Background

The Sun's 11-year magnetic cycle — the cyclic emergence of sunspot groups that drift from about 30 degrees latitude toward the equator (the butterfly diagram) — is produced by a magnetohydrodynamic (MHD) dynamo: motions of the electrically conducting solar plasma weave and regenerate the large-scale magnetic field. In the standard picture, differential rotation stretches the north-south (poloidal) field into east-west (toroidal) field (the Omega effect), while another mechanism regenerates the poloidal component — an alpha effect from helical turbulence in mean-field theory, or, in Babcock-Leighton models, the decay of tilted bipolar active regions whose flux is transported poleward by near-surface flows. Where this loop operates — deep at the tachocline (the shear layer at the base of the convection zone), distributed through the convection zone, or near the surface — is a central unresolved question of solar dynamo theory. Superimposed on the mean solar rotation are torsional oscillations: narrow bands of slightly faster and slower rotation that migrate in lockstep with the sunspot butterfly and evidently share its magnetic cause. Helioseismology, which infers the Sun's interior rotation from its global oscillation frequencies, locates the low-latitude torsional oscillations within the near-surface shear layer (NSSL), the outer roughly 5-10% of the Sun in which angular velocity increases inward. The magnetorotational instability (MRI), best known from accretion-disk theory and realized in laboratory liquid-metal experiments, destabilizes a magnetized, rotating plasma when rotation decreases outward fast enough; in its axisymmetric form the local criterion is $2\Omega S>\omega_A^2$, with $\Omega$ the rotation rate, $S$ the radial shear, and $\omega_A$ the Alfvén frequency (the oscillation frequency of Alfvén waves, the fundamental magnetic-elastic wave of a magnetized conducting fluid) of the field threading the layer. Vasil et al. (2024) noted that the NSSL — inwardly increasing rotation plus a subsurface poloidal field — satisfies the qualitative prerequisites for MRI, and proposed that the solar dynamo is essentially a near-surface instability: at cycle minimum a moderate poloidal field in the NSSL is MRI-unstable, the instability generates the toroidal field and the torsional oscillations, saturates by radial transport of mean magnetic flux and angular momentum, and secondary instabilities regenerate the poloidal field. Analytic estimates and anelastic eigenvalue simulations (the anelastic approximation filters out sound waves while retaining buoyancy-driven dynamics; computed in Dedalus, an open-source spectral code for solving partial differential equations) — with enhanced turbulent diffusivities, that is hydrodynamic and magnetic Reynolds numbers $\mathrm{Re}=\mathrm{Rm}\approx 1500$ (the ratios of advective transport to viscous and to magnetic diffusion) and magnetic Prandtl number $\mathrm{Pm}=1$ (the ratio of the two diffusivities) — reproduce the spatiotemporal scales of the torsional oscillations and the observed hemispheric sign rule of the current helicity $H\propto\mathbf{b}\cdot\nabla\times\mathbf{b}$ (with $\mathbf{b}$ the fluctuating magnetic field). Earlier analyses of MRI in the Sun (Kagan and Wheeler 2014) treated only small horizontal scales; Vasil et al. were the first to consider the large-scale MRI dynamics relevant to the global cycle. The authors themselves delimited what remains unproven: the calculations are linear or quasi-linear with reduced physics (no convective driving, baroclinicity, magnetic buoyancy, partial ionization, or radiative transfer near the photosphere); the diffusivities are turbulent parameterizations far from solar microphysical values ($\mathrm{Re}\sim 10^{12}$, $\mathrm{Pm}\ll 1$); the return step that regenerates the poloidal field is conjectured rather than computed, with candidate routes including helical MRI (the variant driven by a background field with both azimuthal and vertical components), nonaxisymmetric MRI, the clamshell instability of the toroidal field band, and coupling to the surface Babcock-Leighton process; and the whole picture awaits quantitative observational tests.

Problem Statement

Determine whether the near-surface magnetorotational instability can sustain the solar magnetic cycle under realistic, fully nonlinear, turbulent conditions, as posed for future work by Vasil et al. (2024). Concretely: (i) in fully nonlinear three-dimensional stratified MHD simulations of the near-surface shear layer — including convective driving and the observed inwardly increasing differential rotation, not the reduced linear or quasi-linear, enhanced-diffusivity ($\mathrm{Re}=\mathrm{Rm}\approx 1500$, $\mathrm{Pm}=1$) calculations of the source paper — establish whether the axisymmetric MRI operates, what saturates it, and whether its saturation amplitudes and mode scales remain solar-like as the turbulent diffusivities, Reynolds numbers, and magnetic Prandtl number are bridged toward solar values ($\mathrm{Re}\sim 10^{12}$, $\mathrm{Pm}\ll 1$), and as magnetic boundary conditions with open versus closed magnetic-helicity fluxes are varied; and (ii) identify and demonstrate the nonlinear mechanism that regenerates the poloidal field from the MRI-amplified toroidal field — helical or nonaxisymmetric MRI, the clamshell instability of the toroidal band, coupling to the surface Babcock-Leighton process, or another route — closing the poloidal-to-toroidal-to-poloidal loop into a self-sustaining, roughly 11-year cycle in the presence of strong convection. The source additionally proposes observational tests of the hypothesis: joint, time-resolved helioseismic inversions of flows and subsurface magnetic fields could check the predicted correlations between torsional-oscillation flow perturbations and subsurface fields and the poloidal-field strength window outside which the MRI picture fails (a field too strong suppresses the instability; too weak cannot explain the observed torsional oscillations). A complete answer either establishes the near-surface MRI dynamo as the engine of the solar cycle — with its nonlinear saturation, closure mechanism, and parameter robustness demonstrated — or excludes it, identifying the decisive constraint (for example turbulent dissipation, helicity-flux and boundary conditions, the absence of a viable poloidal-regeneration route, or another obstruction). A resolving answer should argue the parameter dependence by extrapolation from the computationally accessible range toward solar values ($\mathrm{Re}\sim 10^{12}$, $\mathrm{Pm}\ll 1$) and address the cycle at the scale of the near-surface shear layer rather than by reproducing the global butterfly diagram; an answer that instead excludes the dynamo must itself demonstrate the decisive constraint under fully nonlinear conditions, rather than merely citing an existing result.

References

1. Vasil, G. M.; Lecoanet, D.; Augustson, K.; Burns, K. J.; Oishi, J. S.; Brown, B. P.; Brummell, N.; Julien, K. The solar dynamo begins near the surface. Nature 629, 769-772 (2024). DOI: 10.1038/s41586-024-07315-1; arXiv:2404.07740. https://doi.org/10.1038/s41586-024-07315-1
2. Brandenburg, A.; Larsson, G.; Del Sordo, F.; Käpylä, P. J. Magnetorotational Instability in a Solar Near-surface Mean-field Dynamo. The Astrophysical Journal 993, 22 (2025). DOI: 10.3847/1538-4357/ae03c4; arXiv:2504.16849. https://doi.org/10.3847/1538-4357/ae03c4
3. Mandal, K.; Kosovichev, A. G. Helioseismic evidence that the solar dynamo originates near the tachocline. Scientific Reports 16, 4222 (2026). DOI: 10.1038/s41598-025-34336-1; arXiv:2601.03238. https://doi.org/10.1038/s41598-025-34336-1
4. Kagan, D.; Wheeler, J. C. The Role of the Magnetorotational Instability in the Sun. The Astrophysical Journal 787, 21 (2014). DOI: 10.1088/0004-637X/787/1/21; arXiv:1407.4654. https://doi.org/10.1088/0004-637X/787/1/21
5. Komm, R.; Howe, R. Solar-Cycle Variation of Large-Scale Flows in the Near-Surface Shear Layer from SC 23 to SC 26. Solar Physics 300, 149 (2025). DOI: 10.1007/s11207-025-02566-1. https://doi.org/10.1007/s11207-025-02566-1
6. Hotta, H. Simultaneous Construction of Fast Equator, Poleward Meridional Flow, and Near-surface Shear Layer in Solar Magnetohydrodynamic Calculation. The Astrophysical Journal 985, 163 (2025). DOI: 10.3847/1538-4357/adca3b; arXiv:2504.05680. https://doi.org/10.3847/1538-4357/adca3b
7. Tripathi, B.; Fraser, A. E.; Terry, P. W.; Zweibel, E. G.; Pueschel, M. J.; Fan, R. Large-scale dynamos driven by shear-flow-induced jets. Nature 649, 848-852 (2026). DOI: 10.1038/s41586-025-09912-0. https://doi.org/10.1038/s41586-025-09912-0
8. Zweibel, E. Instability could explain the Sun's curious cycle. Nature 629, 762-763 (2024). DOI: 10.1038/d41586-024-01357-1. https://doi.org/10.1038/d41586-024-01357-1
9. Gaire, B. Solar dynamo located near the surface. Nature Astronomy 8, 684 (2024). DOI: 10.1038/s41550-024-02311-x. https://doi.org/10.1038/s41550-024-02311-x